"I am not talking to you."
I'm sorry to differ, but "tell to me" certainly is English. It always has a direct object, which is almost always between the verb and the prepositional phrase, so maybe that is what's throwing you off.
I might say, "Will he tell his secret to me?" and I might answer myself, "No, that's a thing he would never tell to me." It puts a bit of emphasis on "me," as though he might tell other people.
I agree with you starting this statement. "Tell to me" only works if you include the direct object. Something like "Tell the story to me" is totally valid. "Tell to me" by itself doesn't make much sense though without a direct object, even if you give it a context.
Oddly enough, you could use either "bana söylemek" or "bana anlatmak" to mean "tell [to/] me"
That seems odd to me, but I suppose it would work similarly to "give me a ball / give a ball to me". (I would say, "Will he tell me his secret? No that's a thing he would never tell me.", emphasising the "me" through voice emphasis only.)
But most commonly, "tell" + preposition is seen with indirect object "me/him/us/etc." rather than with explicit "to" -- in constrast to "say", which, if it has a preposition as recipient, must have "to". You can tell me "good morning" but you cannot say me "good morning", even though you can say "good morning" to me.
If I may... I almost agree with both of you. "That's a thing he would never tell to me" sounds weird to me, too, but I can't prove it's wrong. But I would say it without the "to", just stressing the "me".
On "say" vs "tell", I must say "tell me 'good morning' " is wrong in my opinion. Tell me a joke, tell me a lie, tell me to stop, tell me apart from the others, but, please, >say< "good morning" to me. Or tell me that you want to say "good morning", and then say it. But don't tell anyone. The main difference between "say" and "tell" is that "tell" is usually followed by a personal direct object. We make it clear who we tell. Tell me your secret or just say it.